The number of toy kangaroos, K, in a toy box after 't' days is given by #K=t^2+20t#. Estimate the rate at which the number of kangaroos is changing after 3 days?

#K=t^2+20t#

1 Answer
Apr 13, 2018

Answer:

After 3 days, the number of kangaroos is increasing by 26 kangaroos per day.

Explanation:

The rate of change of a function is the derivative of that function.

First take the derivative of #K=t^2+20t#.
The derivative of #t^n# is #nt^(n-1)# by the power rule.
So the derivative of #t^2# is #2t#.
The derivative of #at# is just #a#, so the derivative of #20t# is just #20#.
You should end up with #K'=2t+20# when you add them together.

The question wants to know the rate of change after 3 days, so just plug in 3:
#K'=2(3)+20#
#K'=26#
So there you have it- after 3 days, the number of kangaroos is increasing by 26 kangaroos per day.